Ans1. The graph y = p(x) intersects the x axis at four points.
So, the polynomial y = p(x) has 4 zeroes. (1 Mark)
Ans2. Let p (x) = x3 + 4x2 + 2x − 1
Then p (1) = (1)3 + 4 (1)2 + 2(1) – 1
= 1 + 4 + 2 -1
= 6
and p (-1) = (-1)3 + 4 (-1)2 + 2(-1) – 1
= -1 + 4 – 2 – 1
= 0
So, -1 is the zero of the polynomial 3 2 x + 4x + 2x − 1 and 1 is not. (1 Mark)
Ans3. Let the quadratic polynomial be ax2+bx + c, and its zeroes be a and b.
We have,
a + b = 3 =
b
a
−
ab = -1 =
c
a
(1 Mark)
c = -a and b = -3a
If a = 1, then c = -1 and b = -3
So, one quadratic polynomial which satisfies the given condition is x2- 3x -1.
So, any quadratic equation of the form k(x2- 3x -1), where k is a real
number, will satisfy the above condition. (1 Mark)
Ans 4. We have,
p(x) = 2x2 + 3x + 1
q(x) = 2x-1
r(x) = 3
From division algorithm we know that,
If p(x) and g(x) are the two polynomials with g(x) ¹ 0, we can find
polynomial q(x) and r(x) such that
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2
p(x) = g(x) x q(x) + r(x) (1 Mark)
On substitution, we get
2x2 + 3x + 1 = g (x) x (2x -1) + 3
2x2 + 3x – 2 = g(x) x (2x-1)
2x2 + 4x – x – 2 = g(x) x (2x-1)
2x (x + 2) -1 (x+ 2) = g(x) x (2x-1)
(2x-1) ( x+ 2) = g(x) x (2x-1)
g(x) = x + 2 (1 Mark)
Ans 5. We have,
x2 − 5 = (x − 5) (x + 5)
[Using identity, 2 2 a − b = (a − b)(a + b) ]
x2-5 =0 x = 5 ,- 5
Therefore, the zeroes of the polynomial 2 x − 5 are 5 and - 5 (1 Mark)
Now,
Sum of zeroes = 5 - 5 = 0 = 2
(coefficient of x)
coefficient of x
−
(1 Mark)
Product of zeroes = 5 x 5 = 5 = 2
cons tant term
coefficient of x
(1 Mark)
Hence the relationship of the coefficients and zeroes of polynomial is verified.
Ans6. We have,
q(x) = x-1
p(x) = 3 x − 2x + 1
1
Mark
2
Dividing p(x) by q (x), we get
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3
2
3
3 2
2
2
x x 1
x 1 x 2x 1
x x
( ) ( )
x 2x 1
x x
( ) ( )
x 1
x 1
( ) ( )
0
+ −
− − +
−
− +
− +
−
− +
− +
− +
+ −
1
1 Marks
2
Here we get, Remainder = 0 (1 Mark)
Therefore, q (x) = x-1 is a factor of the polynomial p(x) = x3 − 2x + 1
Ans7.
We have polynomial p(x) = 2 3x − 5x + 2 and zeroes are a – b and a + b.
We know that,
Sum of zeroes = 2
(coefficient of x)
coefficient of x
−
So, a – b + a + b =
5
3
2a =
5
3
a =
5
6
1
1 Marks
2
Product of zeroes = 2
cons tant term
coefficient of x
So, (a – b) (a + b) =
2
3
a2 – b2 =
2
3
Substituting the value of a in eqn (2)
b2 =
25
36
-
2
3
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4
=
25 24
36
−
=
1
36
1
1 Marks
2
b =
1
6
Therefore, a =
5
6
and b =
1
6
Ans8.
Since the two zeroes are
5
3
and -
5
3
, (x +
5
3
)(x -
5
3
)= 2 5
x
3
− is a factor
of the given polynomial. (1 Mark)
Now, we will find the other two polynomials by long division.
2
2 4 3 2
4 2
3 2
3
2
2
3x 6x 3
5
x 3x 6x 2x 10x 5
3
3x 5x
( ) ( )
6x 3x 10x 5
6x 10x
( ) ( )
3x 5
3x 5
( ) ( )
0
+ +
− + − − −
−
− +
+ − −
−
− +
−
−
− +
1
1 Marks
2
So, 3x4 + 6x3 − 2x2 − 10x − 5 = ( 2 5
x
3
− ) ( 2 3x + 6x + 3)
1
Mark
2
Factorising 2 3x + 6x + 3 gives,
2 3x + 6x + 3= 2 3x + 3x + 3x + 3
= 3x (x+1) + 3(x+1)
1
1 Marks
2
= (3x+3) (x+1)
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5
So, its zeroes are -1 and -3.
1
Mark
2
Therefore, zeroes of the polynomial 3x4 + 6x3 − 2x2 − 10x − 5 are
5
3
,-
5
3
, -
1 and -3. (1 Mark)
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Friday, August 7, 2009
THE SECRET LIFE OF A MATHS QUESTION AN OVERVIEW OF THE ART AND SCIENCE OF PRODUCING EFFECTIVE TEST QUESTIONS IN MATHEMATICS AND NUMERACY
Content
Content.........................................................................................................................................................2
The Secret Life of Maths Questions ...........................................................................................................3
The Technical Language of Item Writing .................................................................................................3
The Ideal Test Item.....................................................................................................................................4
The Fundamental Question of Test Construction: ...................................................................................4
Two Basic Approaches ...............................................................................................................................4
A: “What specific skills/knowledge does student X have?” .....................................................................4
B: “How good, in general, is student X at mathematics?” ........................................................................4
The relation between A and B ...................................................................................................................4
Examples of Approach A and B: ................................................................................................................5
Approach A or Approach B? .................................................................................................................5
Approach A or Approach B? .................................................................................................................5
Multiple Choice...........................................................................................................................................6
Structure of a Multiple Choice Item..........................................................................................................6
Distractor Reasoning Example 1 ...........................................................................................................6
Distractor Reasoning Example 2 ...........................................................................................................7
Distractors Affect the Tested Content of an Item.....................................................................................7
Distractor Reasoning Highlights Faults in an Item..................................................................................8
Distractors Affect the Difficulty of the Item..............................................................................................8
Developing Better Practice.........................................................................................................................9
EAA Papers and Presentations
www.eaa.unsw.edu.au 3 © Educational Assessment Australia
The Secret Life of Maths Questions
Nick Connolly October 2005
This article is an overview of the art and science of producing effective test questions. I will explain some
technical language and discuss key issues. I will also give the reader some tips and guidelines from my
many years of item writing and test construction experience for state testing programmes and maths
competitions.
The Technical Language of Item Writing
Like most fields of work or study, designing tests has generated its own vocabulary. Whilst technical
terms can be off putting they allow for clearer discussion of key concepts.
The first piece of jargon is the word “item”. In common parlance it was what most of us would refer to as
a test question.
Difficulty
“Difficulty” is a term with many related meanings. At a naΓ―ve, intuitive level its meaning is obvious, how
‘hard’ or ‘easy’ an item is. Putting that intuitive meaning into a more scientific context is difficult and the
term ends up meaning two different things that we hope are related:
· The probability that a given student (or group of students) will get an item correct. There are
many measure of this and finding reliable figures is part of the science of educational
measurement and the related field of psychometrics.
· Features of an item that taxes a student’s ability. This second meaning includes such things
as “cognitive load” i.e. the extent to which features of an item tax a students short-term
memory.
Discrimination
“Discrimination” is the primary aspect by which the effectiveness of an item can be judged. It is a
measure of the extent to which an item changes in difficulty for students of greater ability. An item with
low discrimination will be nearly as difficult (or easy) for the students of high ability as it will for the
students of low ability. An item with very high discrimination will be trivial for the most able students but
next to impossible for the least able students taking the test.
Guess
“Guess” is the extent to which a student who doesn’t have the requisite skill, knowledge or ability to
answer the item can still get the item correct or have a higher than expected chance of getting the item
correct. In statistical terms it is the chance of a ‘false positive’ on an item.
Slip
“Slip” is the opposite of guessing i.e., the extent to which a student who does have “Guess” is the extent
to which a student who does have the requisite skill, knowledge or ability to answer the item can still get
the item wrong or have a higher than expected chance of getting the item wrong. In statistical terms it is
the chance of a ‘false negative’ on an item.
Type
With “type” I’m referring to the style of response the item demands from the student. Major types of
items include Multiple Choice and Constructed Response (where the student must write their own
response) sometimes called “Free Response”. This article will look primarily at multiple choice items.
EAA Papers and Presentations
© Educational Assessment Australia 4 www.eaa.unsw.edu.au
The Ideal Test Item
The ideal test item has:
· An appropriate level of difficulty for the test group. Follow the Goldilocks and the Three Bears
principle: Not too hard, not too easy but just right! Items that are too difficult for a group are off
putting for the students and also provide you with little information about their ability.
· An appropriate level of discrimination for the kind of test. This assumes that the majority of items
really are good tests of mathematics. A good maths item won’t discriminate well in a History test.
· As small a guess factor as possible. The reasons for this are obvious but the degree to which this
can be tolerated will vary depending on the nature of the test.
· As small a slip factor as possible. As for guessing the reasons for this are obvious.
· Has content free of external biases. The item avoids ethnic, gender and other stereotypes. The item
is accessible to the cohort in general except in terms of mathematical content.
· And last but not least… It tests mathematics! The content of the item is mathematics (and/or
numeracy)!
The Fundamental Question of Test Construction:
What is the Test For?
· What do you want to find out?
· How reliable do your results need to be?
· What decisions will you make based on the results? What are the STAKES?
· What are you going to report?
Tests can serve multiple purposes but a test should still have a clear objective or objectives. Be aware that
some objective can conflict with each other. Remember also that the students’ attitude towards the test
can affect their performance.
Two Basic Approaches
A: “What specific skills/knowledge does student X have?”
The test needs a narrow focus with several items in a group focusing on very specific skills. Each item
should have a high discrimination, at least within that group of items. Each item will be of similar
difficulty compared with the whole cohort. The ‘ideal’ item would have only two values for a probability
of success, 1 and 0. In other words the fact that a student got the item right should be very strong evidence
that they do have that particular skill or piece of knowledge.
The pattern of answers in this kind of test is very meaningful. The overall score is less meaningful.
Diagnostic quality: gives specific information about skills a student has.
B: “How good, in general, is student X at mathematics?”
The test needs to be broad with a range of items incorporating many skills. Items should have a good
discrimination but not too high. Items can be of a range of difficulties. Degree of success of an item
should vary continuously and gradually for students of different ability.
The pattern of answers in this kind of test is less meaningful. The overall score is very meaningful.
Diagnostic quality: wrong answers can reveal lack of skills.
The relation between A and B
I’m presenting these two approaches as a dichotomy. The reality is that the two aren’t unrelated. We
would hope that somebody who has been accumulating sets of discrete skills will get better in their
overall performance in mathematics. We also assume, and not without reason, that there is a progression
of skills and knowledge in our teaching and our curricula. Also we can make some reasonable
EAA Papers and Presentations
www.eaa.unsw.edu.au 5 © Educational Assessment Australia
assumptions about what skills a student does or does not have by observing any test item so long as it is
well written.
If we had a fundamental theory of mathematics learning in which we fully understood the ways in which
students learn and progress in mathematics these two approaches would amount to the same thing.
However as we lack such a theory (which would probably entail a full understanding of human
intelligence) we can’t assume these two approaches end up telling us quite the same thing.
Examples of Approach A and B:
Consider the following two items in terms of the two approaches to maths tests:
Approach A or Approach B?
Which one of these shapes will tessellate?
[Adapted from Australasian Schools Mathematics Assessment 03Y7Q34]
Judging by Approach A the item has many faults. It appears to be testing familiarity with tessellation but
the problem is very difficult. It could be expected that many students who know what tessellation means
would get the item incorrect. The multiple choice format includes a degree of guessing.
Judging by Approach B the item is better. Students more able, in general, at mathematics are more likely
to get the item correct. A similar item in the 2003 Australasian Schools Mathematics Assessment had a
percentage correct of 55%. The top third of students has a percentage correct of 71%.
Approach A or Approach B?
What is the name of this shape?
Write your answer here: ____________
[Item writing training item]
Judging by Approach A it is quite clear what this item aims to test. There are issues as to whether to
accept spelling mistakes of ‘pentagon’ but few other issues.
EAA Papers and Presentations
© Educational Assessment Australia 6 www.eaa.unsw.edu.au
Judging by Approach B the item has a number of problems. Either you know the answer or you don’t. If
you have never met the word “pentagon” there are no other mathematical skills you can use to find the
answer. The item is a test of vocabulary rather than mathematical ability.
Multiple Choice
Multiple choice items are a sensible choice for tests of general ability. They are easy to administer and
mark but they also provide kinds of information that can be hard to extract from free-response items.
Structure of a Multiple Choice Item
The strength of a multiple choice item lies in the options. The options are the responses a student can
choose from. The correct option is called the ‘key’; the other options are called ‘distractors’ or ‘foils’.
The options can affect nearly all the properties of an item; its difficulty, its discrimination and even what
the item is testing.
It is not uncommon to see in some tests multiple choice items with little thought behind the distractors.
However the distractors provide valuable information on students reasoning only if they have been well
written.
Distractor Reasoning Example 1
What is the reasoning for each option in this item?
Which option would a Year 9 student pick?
This formula converts a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
Which of these formulas converts Celsius to Fahrenheit?
(A)
32
5
= 9 + F C
(B)
32
9
5 F = C +
(C)
( 32)
9
5 F = C +
(D)
( 32)
5
9 F = C +
[Australasian Schools Mathematics Assessment 04 Year 9 Q13]
Each option serves a purpose, primarily to trap errors. In this case only 15% of Year 9 students chose the
key (A). The strongest option was (D) which is correct apart from the superfluous brackets. The least
popular option was (B). It is worth considering what that tells us about a student’s skills and reasoning in
algebra. Note that the percentage correct for this item is less than the 25% you would expect if the
students just guessed. Multiple Choice items are not necessarily “Multiple Guess” items. Well
constructed items in a well constructed test will minimise guessing. A multiple choice test with several
items such that the least able students stand a better chance of getting the item correct by attempting it
than they would by guessing will effectively penalise guessing. This doesn’t require complicated scoring
systems (such as penalising wrong answers) just a good spread of well written items.
EAA Papers and Presentations
www.eaa.unsw.edu.au 7 © Educational Assessment Australia
Distractor Reasoning Example 2
What would be the best options for this number puzzle?
A zookeeper had some peanuts for the monkeys.
He gave each monkey 4 peanuts and had 2 peanuts left over.
To give each monkey 6 peanuts, he would need another 22 peanuts.
How many monkeys are in the zoo?
[Australasian Schools Mathematics Assessment 04 Year 6 QF3]
The top 6 responses for this item were:
12 26.34% 5 10.93%
11 22.10% 6 10.10%
4 21.96% 3 8.57%
As an exercise try and work out the reasoning behind each response.
Distractors Affect the Tested Content of an Item
What content is tested in this item? Are the distractors suitable? What would be a better set of distractors?
What is the value of a to the nearest whole number?
(A) 10 (B) 10.5
(C) 10.6 (D) 11
[Item writing training item]
This is an artificial example to demonstrate the role of distractors.
The correct answer can be found using Pythagoras (202-172=111, √111=10.535653752….)
Each distractor is based on incorrectly rounding the square root of a hundred and eleven. Consequently
the apparent content of the item (Pythagoras) is barely tested and the main focus of the item is rounding
and knowing what ‘to the nearest whole number’ means. Note that a student who only knows what ‘to the
nearest whole number’ means can eliminate two of the options straight away.
17 cm
20 cm
a cm
EAA Papers and Presentations
© Educational Assessment Australia 8 www.eaa.unsw.edu.au
Distractor Reasoning Highlights Faults in an Item
What is the reasoning behind each of these, numerically identical, options?
How should the item be rewritten?
What is the value of 22?
(A) 4
(B) 4
(C) 4
[Item writing training item]
A possible set of distractors for testing whether students are familiar with the square notation would be to
give options based on possible interpretations. In the example these are:
· 2+2=4
· 2´2=4
· 2 squared =4 (the key)
Clearly nobody would pick 22 as the example to use to test that skill! However less trivial items can suffer
from incorrect but plausible methods that lead to the correct answer. This is not always obvious until you
consider what plausible strategies a student might take to answer the item.
Even on free response items it is worth considering what would be the most appropriate set of distractors.
Distractors Affect the Difficulty of the Item
About 60% of Year 8 students could answer this question in a maths competition.
What set of options would have made the item harder? How could we change only the options of this
item to test a related but different skill?
The picture shows the angle between two sections of a roof.
Which of these is the best estimate of the value of a?
(A) 90
(B) 100
(C) 120
(D) 140
[Australasian Schools Mathematics Assessment 05 Y8 Q23]
The difficulty of estimation questions clearly depends to some extent on the options.
This set of options would have been much more challenging as they demand greater precision:
(A) 130
(B) 135
(C) 140
(D) 145
EAA Papers and Presentations
www.eaa.unsw.edu.au 9 © Educational Assessment Australia
This set of options changes the item from estimation to recognition of an obtuse angle:
(A) 40
(B) 90
(C) 140
(D) 240
For anybody who is interested the picture is of Trial Bay Gaol near Arrakoon NSW.
Developing Better Practice
Developing good test items helps clarify your own thinking about the curriculum and assessment. Taking
care to write well structured items will improve the quality of the data you obtain from tests. The
following 4 points sum up the major ways the quality of test items you use can be maintained or
improved:
1. Be clear about what kind of data you want from your tests
2. Choose and write items suitable for the kind of test you are writing
3. Maintain a bank of items you have developed
4. Look at how items have performed over time and use that data to refine the items you have.
Finally remember that if you aren’t enjoying writing an item you can be quite sure your students won’t be
enjoying answering it.
Content.........................................................................................................................................................2
The Secret Life of Maths Questions ...........................................................................................................3
The Technical Language of Item Writing .................................................................................................3
The Ideal Test Item.....................................................................................................................................4
The Fundamental Question of Test Construction: ...................................................................................4
Two Basic Approaches ...............................................................................................................................4
A: “What specific skills/knowledge does student X have?” .....................................................................4
B: “How good, in general, is student X at mathematics?” ........................................................................4
The relation between A and B ...................................................................................................................4
Examples of Approach A and B: ................................................................................................................5
Approach A or Approach B? .................................................................................................................5
Approach A or Approach B? .................................................................................................................5
Multiple Choice...........................................................................................................................................6
Structure of a Multiple Choice Item..........................................................................................................6
Distractor Reasoning Example 1 ...........................................................................................................6
Distractor Reasoning Example 2 ...........................................................................................................7
Distractors Affect the Tested Content of an Item.....................................................................................7
Distractor Reasoning Highlights Faults in an Item..................................................................................8
Distractors Affect the Difficulty of the Item..............................................................................................8
Developing Better Practice.........................................................................................................................9
EAA Papers and Presentations
www.eaa.unsw.edu.au 3 © Educational Assessment Australia
The Secret Life of Maths Questions
Nick Connolly October 2005
This article is an overview of the art and science of producing effective test questions. I will explain some
technical language and discuss key issues. I will also give the reader some tips and guidelines from my
many years of item writing and test construction experience for state testing programmes and maths
competitions.
The Technical Language of Item Writing
Like most fields of work or study, designing tests has generated its own vocabulary. Whilst technical
terms can be off putting they allow for clearer discussion of key concepts.
The first piece of jargon is the word “item”. In common parlance it was what most of us would refer to as
a test question.
Difficulty
“Difficulty” is a term with many related meanings. At a naΓ―ve, intuitive level its meaning is obvious, how
‘hard’ or ‘easy’ an item is. Putting that intuitive meaning into a more scientific context is difficult and the
term ends up meaning two different things that we hope are related:
· The probability that a given student (or group of students) will get an item correct. There are
many measure of this and finding reliable figures is part of the science of educational
measurement and the related field of psychometrics.
· Features of an item that taxes a student’s ability. This second meaning includes such things
as “cognitive load” i.e. the extent to which features of an item tax a students short-term
memory.
Discrimination
“Discrimination” is the primary aspect by which the effectiveness of an item can be judged. It is a
measure of the extent to which an item changes in difficulty for students of greater ability. An item with
low discrimination will be nearly as difficult (or easy) for the students of high ability as it will for the
students of low ability. An item with very high discrimination will be trivial for the most able students but
next to impossible for the least able students taking the test.
Guess
“Guess” is the extent to which a student who doesn’t have the requisite skill, knowledge or ability to
answer the item can still get the item correct or have a higher than expected chance of getting the item
correct. In statistical terms it is the chance of a ‘false positive’ on an item.
Slip
“Slip” is the opposite of guessing i.e., the extent to which a student who does have “Guess” is the extent
to which a student who does have the requisite skill, knowledge or ability to answer the item can still get
the item wrong or have a higher than expected chance of getting the item wrong. In statistical terms it is
the chance of a ‘false negative’ on an item.
Type
With “type” I’m referring to the style of response the item demands from the student. Major types of
items include Multiple Choice and Constructed Response (where the student must write their own
response) sometimes called “Free Response”. This article will look primarily at multiple choice items.
EAA Papers and Presentations
© Educational Assessment Australia 4 www.eaa.unsw.edu.au
The Ideal Test Item
The ideal test item has:
· An appropriate level of difficulty for the test group. Follow the Goldilocks and the Three Bears
principle: Not too hard, not too easy but just right! Items that are too difficult for a group are off
putting for the students and also provide you with little information about their ability.
· An appropriate level of discrimination for the kind of test. This assumes that the majority of items
really are good tests of mathematics. A good maths item won’t discriminate well in a History test.
· As small a guess factor as possible. The reasons for this are obvious but the degree to which this
can be tolerated will vary depending on the nature of the test.
· As small a slip factor as possible. As for guessing the reasons for this are obvious.
· Has content free of external biases. The item avoids ethnic, gender and other stereotypes. The item
is accessible to the cohort in general except in terms of mathematical content.
· And last but not least… It tests mathematics! The content of the item is mathematics (and/or
numeracy)!
The Fundamental Question of Test Construction:
What is the Test For?
· What do you want to find out?
· How reliable do your results need to be?
· What decisions will you make based on the results? What are the STAKES?
· What are you going to report?
Tests can serve multiple purposes but a test should still have a clear objective or objectives. Be aware that
some objective can conflict with each other. Remember also that the students’ attitude towards the test
can affect their performance.
Two Basic Approaches
A: “What specific skills/knowledge does student X have?”
The test needs a narrow focus with several items in a group focusing on very specific skills. Each item
should have a high discrimination, at least within that group of items. Each item will be of similar
difficulty compared with the whole cohort. The ‘ideal’ item would have only two values for a probability
of success, 1 and 0. In other words the fact that a student got the item right should be very strong evidence
that they do have that particular skill or piece of knowledge.
The pattern of answers in this kind of test is very meaningful. The overall score is less meaningful.
Diagnostic quality: gives specific information about skills a student has.
B: “How good, in general, is student X at mathematics?”
The test needs to be broad with a range of items incorporating many skills. Items should have a good
discrimination but not too high. Items can be of a range of difficulties. Degree of success of an item
should vary continuously and gradually for students of different ability.
The pattern of answers in this kind of test is less meaningful. The overall score is very meaningful.
Diagnostic quality: wrong answers can reveal lack of skills.
The relation between A and B
I’m presenting these two approaches as a dichotomy. The reality is that the two aren’t unrelated. We
would hope that somebody who has been accumulating sets of discrete skills will get better in their
overall performance in mathematics. We also assume, and not without reason, that there is a progression
of skills and knowledge in our teaching and our curricula. Also we can make some reasonable
EAA Papers and Presentations
www.eaa.unsw.edu.au 5 © Educational Assessment Australia
assumptions about what skills a student does or does not have by observing any test item so long as it is
well written.
If we had a fundamental theory of mathematics learning in which we fully understood the ways in which
students learn and progress in mathematics these two approaches would amount to the same thing.
However as we lack such a theory (which would probably entail a full understanding of human
intelligence) we can’t assume these two approaches end up telling us quite the same thing.
Examples of Approach A and B:
Consider the following two items in terms of the two approaches to maths tests:
Approach A or Approach B?
Which one of these shapes will tessellate?
[Adapted from Australasian Schools Mathematics Assessment 03Y7Q34]
Judging by Approach A the item has many faults. It appears to be testing familiarity with tessellation but
the problem is very difficult. It could be expected that many students who know what tessellation means
would get the item incorrect. The multiple choice format includes a degree of guessing.
Judging by Approach B the item is better. Students more able, in general, at mathematics are more likely
to get the item correct. A similar item in the 2003 Australasian Schools Mathematics Assessment had a
percentage correct of 55%. The top third of students has a percentage correct of 71%.
Approach A or Approach B?
What is the name of this shape?
Write your answer here: ____________
[Item writing training item]
Judging by Approach A it is quite clear what this item aims to test. There are issues as to whether to
accept spelling mistakes of ‘pentagon’ but few other issues.
EAA Papers and Presentations
© Educational Assessment Australia 6 www.eaa.unsw.edu.au
Judging by Approach B the item has a number of problems. Either you know the answer or you don’t. If
you have never met the word “pentagon” there are no other mathematical skills you can use to find the
answer. The item is a test of vocabulary rather than mathematical ability.
Multiple Choice
Multiple choice items are a sensible choice for tests of general ability. They are easy to administer and
mark but they also provide kinds of information that can be hard to extract from free-response items.
Structure of a Multiple Choice Item
The strength of a multiple choice item lies in the options. The options are the responses a student can
choose from. The correct option is called the ‘key’; the other options are called ‘distractors’ or ‘foils’.
The options can affect nearly all the properties of an item; its difficulty, its discrimination and even what
the item is testing.
It is not uncommon to see in some tests multiple choice items with little thought behind the distractors.
However the distractors provide valuable information on students reasoning only if they have been well
written.
Distractor Reasoning Example 1
What is the reasoning for each option in this item?
Which option would a Year 9 student pick?
This formula converts a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
Which of these formulas converts Celsius to Fahrenheit?
(A)
32
5
= 9 + F C
(B)
32
9
5 F = C +
(C)
( 32)
9
5 F = C +
(D)
( 32)
5
9 F = C +
[Australasian Schools Mathematics Assessment 04 Year 9 Q13]
Each option serves a purpose, primarily to trap errors. In this case only 15% of Year 9 students chose the
key (A). The strongest option was (D) which is correct apart from the superfluous brackets. The least
popular option was (B). It is worth considering what that tells us about a student’s skills and reasoning in
algebra. Note that the percentage correct for this item is less than the 25% you would expect if the
students just guessed. Multiple Choice items are not necessarily “Multiple Guess” items. Well
constructed items in a well constructed test will minimise guessing. A multiple choice test with several
items such that the least able students stand a better chance of getting the item correct by attempting it
than they would by guessing will effectively penalise guessing. This doesn’t require complicated scoring
systems (such as penalising wrong answers) just a good spread of well written items.
EAA Papers and Presentations
www.eaa.unsw.edu.au 7 © Educational Assessment Australia
Distractor Reasoning Example 2
What would be the best options for this number puzzle?
A zookeeper had some peanuts for the monkeys.
He gave each monkey 4 peanuts and had 2 peanuts left over.
To give each monkey 6 peanuts, he would need another 22 peanuts.
How many monkeys are in the zoo?
[Australasian Schools Mathematics Assessment 04 Year 6 QF3]
The top 6 responses for this item were:
12 26.34% 5 10.93%
11 22.10% 6 10.10%
4 21.96% 3 8.57%
As an exercise try and work out the reasoning behind each response.
Distractors Affect the Tested Content of an Item
What content is tested in this item? Are the distractors suitable? What would be a better set of distractors?
What is the value of a to the nearest whole number?
(A) 10 (B) 10.5
(C) 10.6 (D) 11
[Item writing training item]
This is an artificial example to demonstrate the role of distractors.
The correct answer can be found using Pythagoras (202-172=111, √111=10.535653752….)
Each distractor is based on incorrectly rounding the square root of a hundred and eleven. Consequently
the apparent content of the item (Pythagoras) is barely tested and the main focus of the item is rounding
and knowing what ‘to the nearest whole number’ means. Note that a student who only knows what ‘to the
nearest whole number’ means can eliminate two of the options straight away.
17 cm
20 cm
a cm
EAA Papers and Presentations
© Educational Assessment Australia 8 www.eaa.unsw.edu.au
Distractor Reasoning Highlights Faults in an Item
What is the reasoning behind each of these, numerically identical, options?
How should the item be rewritten?
What is the value of 22?
(A) 4
(B) 4
(C) 4
[Item writing training item]
A possible set of distractors for testing whether students are familiar with the square notation would be to
give options based on possible interpretations. In the example these are:
· 2+2=4
· 2´2=4
· 2 squared =4 (the key)
Clearly nobody would pick 22 as the example to use to test that skill! However less trivial items can suffer
from incorrect but plausible methods that lead to the correct answer. This is not always obvious until you
consider what plausible strategies a student might take to answer the item.
Even on free response items it is worth considering what would be the most appropriate set of distractors.
Distractors Affect the Difficulty of the Item
About 60% of Year 8 students could answer this question in a maths competition.
What set of options would have made the item harder? How could we change only the options of this
item to test a related but different skill?
The picture shows the angle between two sections of a roof.
Which of these is the best estimate of the value of a?
(A) 90
(B) 100
(C) 120
(D) 140
[Australasian Schools Mathematics Assessment 05 Y8 Q23]
The difficulty of estimation questions clearly depends to some extent on the options.
This set of options would have been much more challenging as they demand greater precision:
(A) 130
(B) 135
(C) 140
(D) 145
EAA Papers and Presentations
www.eaa.unsw.edu.au 9 © Educational Assessment Australia
This set of options changes the item from estimation to recognition of an obtuse angle:
(A) 40
(B) 90
(C) 140
(D) 240
For anybody who is interested the picture is of Trial Bay Gaol near Arrakoon NSW.
Developing Better Practice
Developing good test items helps clarify your own thinking about the curriculum and assessment. Taking
care to write well structured items will improve the quality of the data you obtain from tests. The
following 4 points sum up the major ways the quality of test items you use can be maintained or
improved:
1. Be clear about what kind of data you want from your tests
2. Choose and write items suitable for the kind of test you are writing
3. Maintain a bank of items you have developed
4. Look at how items have performed over time and use that data to refine the items you have.
Finally remember that if you aren’t enjoying writing an item you can be quite sure your students won’t be
enjoying answering it.
Maths Questions Chapter 2 Polynomials Time Allowed: 1 Hr Maximum Marks: 20
Maths Questions
Chapter 2 Polynomials
Time Allowed: 1 Hr Maximum Marks: 20
_____________________________________________________________
1. All questions are compulsory.
2. The question paper consist of 8 questions
3. Questions 1 and 2 are very short questions of 1 mark each questions 3 to
5 are short questions carrying 2 marks each questions 6 to 7 are short
questions carrying 3 marks each and question number 8 is very long
question carrying 6 marks
4. There is no overall choice.
5. Use of calculators is not permitted.
Q1. Find the zeroes of the polynomial p(x) =2x-5.
(1 mark)
Q2. Check whether -2 and 2 are the zeroes of the polynomial 3 x − 8 .
(1 mark)
Q3. Evaluate 497 X 503
(2 marks)
Q4. Without actual division find the remainder, when the polynomial
3 2 4x − 3x + 2x − 4 is divided by
1
x
2
+
.
(2 marks)
Q5. Without calculating cubes, find the value of (-12)3 + (7)3 + (5)3.
(2 marks)
Q6. If 2 x + px + q = (x + a)(x + b) , then factorise 2 2 x + pxy + qy .
(3 marks)
Q7. Factorise: 3 2 2y + y − 2y − 1
(3 marks)
Get the Power of Visual Impact on your side
Log on to www.topperlearning.com
2
Q8. What are the possible expressions for the dimensions of the cuboids
whose volume is given by 3 2 x − 3x − 9x − 5
(6 marks)
Chapter 2 Polynomials
Time Allowed: 1 Hr Maximum Marks: 20
_____________________________________________________________
1. All questions are compulsory.
2. The question paper consist of 8 questions
3. Questions 1 and 2 are very short questions of 1 mark each questions 3 to
5 are short questions carrying 2 marks each questions 6 to 7 are short
questions carrying 3 marks each and question number 8 is very long
question carrying 6 marks
4. There is no overall choice.
5. Use of calculators is not permitted.
Q1. Find the zeroes of the polynomial p(x) =2x-5.
(1 mark)
Q2. Check whether -2 and 2 are the zeroes of the polynomial 3 x − 8 .
(1 mark)
Q3. Evaluate 497 X 503
(2 marks)
Q4. Without actual division find the remainder, when the polynomial
3 2 4x − 3x + 2x − 4 is divided by
1
x
2
+
.
(2 marks)
Q5. Without calculating cubes, find the value of (-12)3 + (7)3 + (5)3.
(2 marks)
Q6. If 2 x + px + q = (x + a)(x + b) , then factorise 2 2 x + pxy + qy .
(3 marks)
Q7. Factorise: 3 2 2y + y − 2y − 1
(3 marks)
Get the Power of Visual Impact on your side
Log on to www.topperlearning.com
2
Q8. What are the possible expressions for the dimensions of the cuboids
whose volume is given by 3 2 x − 3x − 9x − 5
(6 marks)
Engineers Zone Aptitude Questions
Solve the following and check with the answers given at the end.
1. It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
2. A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
3. A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.
4. A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?
5. A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.
6. A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.
7. what is a percent of b divided by b percent of a?
(a) a (b) b (c) 1 (d) 10 (d) 100
8. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
9. A tennis marker is trying to put together a team of four players for a tennis tournament out of seven available. males - a, b and c; females – m, n, o and p. All players are of equal ability and there must be at least two males in the team. For a team of four, all players must be able to play with each other under the following restrictions:
b should not play with m,
c should not play with p, and
a should not play with o.
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Engineers Zone
Which of the following statements must be false?
1. b and p cannot be selected together
2. c and o cannot be selected together
3. c and n cannot be selected together.
10-12. The following figure depicts three views of a cube. Based on this, answer questions 10-12.
6 5 4
1 22 3 6
2
2
3
10. The number on the face opposite to the face carrying 1 is _______ .
11. The number on the faces adjacent to the face marked 5 are _______ .
12. Which of the following pairs does not correctly give the numbers on the opposite faces.
(1) 6,5 (2) 4,1 (3) 1,3 (4) 4,2
13. Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
14. Five boys were climbing a hill. J was following H. R was just ahead of G. K was between G & H. They were climbing up in a column. Who was the second?
15-18 John is undecided which of the four novels to buy. He is considering a spy
thriller, a Murder mystery, a Gothic romance and a science fiction novel. The books are written by Rothko, Gorky, Burchfield and Hopper, not necessary in that order, and published by Heron, Piegon, Blueja and sparrow, not necessary in that order.
(1) The book by Rothko is published by Sparrow.
(2) The Spy thriller is published by Heron.
(3) The science fiction novel is by Burchfield and is not published by Blueja.
(4)The Gothic romance is by Hopper.
15. Pigeon publishes ____________.
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Engineers Zone
16. The novel by Gorky ________________.
17. John purchases books by the authors whose names come first and third in alphabetical order. He does not buy the books ______.
18. On the basis of the first paragraph and statement (2), (3) and (4) only, it is possible to deduce that
1. Rothko wrote the murder mystery or the spy thriller
2. Sparrow published the murder mystery or the spy thriller
3. The book by Burchfield is published by Sparrow.
19. If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?
20. If point P is on line segment AB, then which of the following is always true?
(1) AP = PB (2) AP > PB (3) PB > AP (4) AB > AP (5) AB > AP + PB
21. All men are vertebrates. Some mammals are vertebrates. Which of the following conclusions drawn from the above statement is correct.
All men are mammals
All mammals are men
Some vertebrates are mammals.
None
22. Which of the following statements drawn from the given statements are correct?
Given:
All watches sold in that shop are of high standard. Some of the HMT watches are sold in that shop.
a) All watches of high standard were manufactured by HMT.
b) Some of the HMT watches are of high standard.
c) None of the HMT watches is of high standard.
d) Some of the HMT watches of high standard are sold in that shop.
23-27.
1. Ashland is north of East Liverpool and west of Coshocton.
2. Bowling green is north of Ashland and west of Fredericktown.
3. Dover is south and east of Ashland.
4. East Liverpool is north of Fredericktown and east of Dover.
5. Fredericktown is north of Dover and west of Ashland.
6. Coshocton is south of Fredericktown and west of Dover.
23. Which of the towns mentioned is furthest of the north – west
(a) Ashland (b) Bowling green (c) Coshocton
(d) East Liverpool (e) Fredericktown
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Engineers Zone
24. Which of the following must be both north and east of Fredericktown?
(a) Ashland (b) Coshocton (c) East Liverpool
I a only II b only III c only IV a & b V a & c
25. Which of the following towns must be situated both south and west of at least one other town?
A. Ashland only
B. Ashland and Fredericktown
C. Dover and Fredericktown
D. Dover, Coshocton and Fredericktown
E. Coshocton, Dover and East Liverpool.
26. Which of the following statements, if true, would make the information in the numbered statements more specific?
(a) Coshocton is north of Dover.
(b) East Liverpool is north of Dover
(c) Ashland is east of Bowling green.
(d) Coshocton is east of Fredericktown
(e) Bowling green is north of Fredericktown
27. Which of the numbered statements gives information that can be deduced from one or more of the other statements?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 6
28. Eight friends Harsha, Fakis, Balaji, Eswar, Dhinesh, Chandra, Geetha, and Ahmed are sitting in a circle facing the center. Balaji is sitting between Geetha and Dhinesh. Harsha is third to the left of Balaji and second to the right of Ahmed. Chandra is sitting between Ahmed and Geetha and Balaji and Eshwar are not sitting opposite to each other. Who is third to the left of Dhinesh?
29. If every alternative letter starting from B of the English alphabet is written in small letter, rest all are written in capital letters, how the month “ September” be written.
(1) SeptEMbEr (2) SEpTeMBEr (3) SeptembeR
(4) SepteMber (5) None of the above.
30. The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______.
31. It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?
32. Which of the following is larger than 3/5? 4
Engineers Zone
(1) ½ (2) 39/50 (3) 7/25 (4) 3/10 (5) 59/100
33. The number that does not have a reciprocal is ____________.
34. There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.
35. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
Answers:
1. Answer:
30 days.
Explanation:
Before:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work = (75 * 20) / 50 = 30
2. Answer:
0 %
Explanation:
Since 3x / 2 = x / (2 / 3)
3. Answer:
5.3 %
Explanation:
He sells 950 grams of pulses and gains 50 grams.
If he sells 100 grams of pulses then he will gain (50 / 950) *100 = 5.26
4. Answer:
250 lines of codes
5. Answer:
7 days
Explanation:
The equation portraying the given problem is:
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Engineers Zone
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.
6. Answer:
150 men.
Explanation:
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)
The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.
So we get the equation
(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working after the 90th day.
We get x = 225
Since we have 75 men already, it is enough to add only 150 men.
7. Answer:
(c) 1
Explanation:
a percent of b : (a/100) * b
b percent of a : (b/100) * a
a percent of b divided by b percent of a : ((a / 100 )*b) / (b/100) * a )) = 1
8. Answer:
Cost price of horse = Rs. 400 & the cost price of cart = 200.
Explanation:-
Let x be the cost price of the horse and y be the cost price of the cart.
In the first sale there is no loss or profit. (i.e.) The loss obtained is equal to the gain.
Therefore (10/100) * x = (20/100) * y
X = 2 * y -----------------(1)
In the second sale, he lost Rs. 10. (i.e.) The loss is greater than the profit by Rs. 10.
Therefore (5 / 100) * x = (5 / 100) * y + 10 -------(2)
Substituting (1) in (2) we get
(10 / 100) * y = (5 / 100) * y + 10
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Engineers Zone
(5 / 100) * y = 10
y = 200
From (1) 2 * 200 = x = 400
9. Answer:
3.
Explanation:
Since inclusion of any male player will reject a female from the team. Since there should be four member in the team and only three males are available, the girl, n should included in the team always irrespective of others selection.
10. Answer:
5
11. Answer:
1,2,3 & 4
12. Answer:
B
13. Answer:
11 & 9 apples per tree.
Explanation:
Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that a + 1 = b + 3 = c – 1 = d + 3 = e – 6
But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3.
Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively.
Therefore 11 x – 1 = 13 y + 3
By trial and error method, we get the value for x and y as 11 and 9
14. Answer:
G.
Explanation:
The order in which they are climbing is R – G – K – H – J
15 – 18
Answer:
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow
7
Engineers Zone
Explanation:
Given
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow
Since Blueja doesn’t publish the novel by Burchfield and Heron publishes the novel spy thriller, Piegon publishes the novel by Burchfield.
Since Hopper writes Gothic romance and Heron publishes the novel spy thriller, Blueja publishes the novel by Hopper.
Since Heron publishes the novel spy thriller and Heron publishes the novel by Gorky, Gorky writes Spy thriller and Rathko writes Murder mystery.
19. Answer:
451 times.
Explanation:
There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
20. Answer:
(4)
Explanation:
P
A B
Since p is a point on the line segment AB, AB > AP
21. Answer: (c)
22. Answer: (b) & (d).
Ahmed
23 - 27.Answer:
Fakis Chandra
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Engineers Zone
28. Answer:Fakis
Explanation: Harsha Geetha
Eswar Balaji
Dhinesh
29. Answer:
(5).
Explanation:
Since every alternative letter starting from B of the English alphabet is written in small letter, the letters written in small letter are b, d, f...
In the first two answers the letter E is written in both small & capital letters, so they are not the correct answers. But in third and fourth answers the letter is written in small letter instead capital letter, so they are not the answers.
30. Answer:
x = 4
Explanation:
Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
(i.e.) 4x + 8 = 6x
(i.e.) 2x = 8 τ x = 4.
31. Answer:
(y – 2) / y.
Explanation:
To type a manuscript karthik took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y
32. Answer:
(2)
33. Answer:
1
Explanation:
One is the only number exists without reciprocal because the reciprocal of one is one itself.
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Engineers Zone
34. Answer:
Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars.
Explanation:
Sudhir Arvind Gauri
Finally 24 24 24
Before Gauri’s transaction 12 12 48
Before Arvind’s transaction 6 42 24
Before Sudhir’ s transaction 39 21 12
35. Answer:
Cost price of horse: Rs. 400 &
Cost price of cart: Rs. 200
Explanation:
Let x be the cost of horse & y be the cost of the cart.
10 % of loss in selling horse = 20 % of gain in selling the cart
Therefore (10 / 100) * x = (20 * 100) * y
τ x = 2y -----------(1)
5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart.
Therefore (5 / 100) * x - 10 = (5 / 100) * y
τ 5x - 1000 = 5y
Substituting (1)
10y - 1000 = 5y
5y = 1000
y = 200
x = 400 from (1)
Exercise 2.1
For the following, find the next term in the series
1. 6, 24, 60,120, 210
a) 336 b) 366 c) 330 d) 660
Answer : a) 336
Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ..... ( '.' means product)
2. 1, 5, 13, 25
Answer : 41
Explanation : The series is of the form 0^2+1^2, 1^2+2^2,...
3. 0, 5, 8, 17
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Engineers Zone
Answer : 24
Explanation : 1^2-1, 2^2+1, 3^2-1, 4^2+1, 5^2-1
4. 1, 8, 9, 64, 25 (Hint : Every successive terms are related)
Answer : 216
Explanation : 1^2, 2^3, 3^2, 4^3, 5^2, 6^3
5. 8,24,12,36,18,54
Answer : 27
6. 71,76,69,74,67,72
Answer : 67
7. 5,9,16,29,54
Answer : 103
Explanation : 5*2-1=9; 9*2-2=16; 16*2-3=29; 29*2-4=54; 54*2-5=103
8. 1,2,4,10,16,40,64 (Successive terms are related)
Answer : 200
Explanation : The series is powers of 2 (2^0,2^1,..).
All digits are less than 8. Every second number is in octal number system.
128 should follow 64. 128 base 10 = 200 base 8.
Exercise 2.2
Find the odd man out.
1. 3,5,7,12,13,17,19
Answer : 12
Explanation : All but 12 are odd numbers
2. 2,5,10,17,26,37,50,64
Answer : 64
Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65;
3. 105,85,60,30,0,-45,-90
Answer : 0
Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90;
Exercise 3
Solve the following.
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Engineers Zone
1. What is the number of zeros at the end of the product of the numbers from 1 to 100?
Answer : 127
2. A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
Answer : 1 hr 12 min
Explanation : The fast typist's work done in 1 hr = 1/2
The slow typist's work done in 1 hr = 1/3
If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min
3. Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)
Answer : 101
Explanation : Total score after 50 innings = 50*50 = 2500
Total score after 51 innings = 51*51 = 2601
So, runs made in the 51st innings = 2601-2500 = 101
If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.
4. Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?
Answer : 4
5. What can you conclude from the statement : All green are blue, all blue are red. ?
(i) some blue are green
(ii) some red are green
(iii) some green are not red
(iv) all red are blue
(a) i or ii but not both
(b) i & ii only
(c) iii or iv but not both
(d) iii & iv
Answer : (b)
6. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?
Answer : 3.5 inches
Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate
(22/7)*4*4*h = 8*11*2
h = 7/2 = 3.5
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7. What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?
Answer : 35392
Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed.
The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.
112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392
8. If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ...... upto infinity.
Answer : 4
Explanation : Let x = s(12+s(12+s(12+.....
We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.
9. A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?
Answer : 16/3 inches
Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased.
So, the effect on increasing height is equal to the effect on increasing the radius.
i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3
Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches.
10. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?
Answer : 1, 3, 9, 27, 81, 243 (All powers of 3)
11. Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus?
Answer : 84 years
Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
12 . If time at this moment is 9 P.M., what will be the time 23999999992 hours later?
Answer : 1 P.M.
Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M.
13. How big will an angle of one and a half degree look through a glass that magnifies things three times?
Answer : 1 1/2 degrees
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Explanation : The magnifying glass cannot increase the magnitude of an angle.
14. Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number.
Answer: 8, 12, 5, 20
Explanation: a + b + c + d =45; a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2); b-4 + b + (b-2)/2 + 2(b-2) = 45;
15. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.
Answer : 37 1/2
Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min
Avg speed = (60*120)/192 = 37 1/2
Questions 16 and 17 are based on the following :
Five executives of European Corporation hold a Conference in Rome
Mr. A converses in Spanish & Italian
Mr. B, a spaniard, knows English also
Mr. C knows English and belongs to Italy
Mr. D converses in French and Spanish
Mr. E , a native of Italy knows French
16. Which of the following can act as interpreter if Mr. C & Mr. D wish to converse
a) only Mr. A b) Only Mr. B c) Mr. A & Mr. B d) Any of the other three
Answer : d) Any of the other three.
Explanation : From the data given, we can infer the following.
A knows Spanish, Italian
B knows Spanish, English
C knows Italian, English
D knows Spanish, French
E knows Italian, French
To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish, English&French
A, B, and E know atleast one of the combinations.
17. If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in
a) English & French b) Italian & Spanish c) English & French d) French & Italian
Answer : b) Italian & Spanish
Explanation : No of executives who know
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i) English is 2
ii) Spanish is 3
iii) Italian is 3
iv) French is 2
Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian.
18. What is the sum of the first 25 natural odd numbers?
Answer : 625
Explanation : The sum of the first n natural odd nos is square(n).
1+3 = 4 = square(2) 1+3+5 = 9 = square(3)
19. The sum of any seven consecutive numbers is divisible by
a) 2 b) 7 c) 3 d) 11
Exercise 3
Try the following.
1. There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25?
2. A man sailed off from the North Pole. After covering 2,000 miles in one direction he turned West, sailed 2,000 miles, turned North and sailed ahead another 2,000 miles till he met his friend. How far was he from the North Pole and in what direction?
3. Here is a series of comments on the ages of three persons J, R, S by themselves.
S : The difference between R's age and mine is three years.
J : R is the youngest.
R : Either I am 24 years old or J 25 or S 26.
J : All are above 24 years of age.
S : I am the eldest if and only if R is not the youngest.
R : S is elder to me.
J : I am the eldest.
R : S is not 27 years old.
S : The sum of my age and J's is two more than twice R's age.
One of the three had been telling a lie throughout whereas others had spoken the truth. Determine the ages of S,J,R.
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4. In a group of five people, what is the probability of finding two persons with the same month of birth?
5. A father and his son go out for a 'walk-and-run' every morning around a track formed by an equilateral triangle. The father's walking speed is 2 mph and his running speed is 5 mph. The son's walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other?
6. The Director of Medical Services was on his annual visit to the ENT Hospital. While going through the out patients' records he came across the following data for a particular day : " Ear consultations 45; Nose 50; Throat 70; Ear and Nose 30; Nose and Throat 20; Ear and Throat 30; Ear, Nose and Throat 10; Total patients 100." Then he came to the conclusion that the records were bogus. Was he right?
7. Amongst Ram, Sham and Gobind are a doctor, a lawyer and a police officer. They are married to Radha, Gita and Sita (not in order). Each of the wives have a profession. Gobind's wife is an artist. Ram is not married to Gita. The lawyer's wife is a teacher. Radha is married to the police officer. Sita is an expert cook. Who's who?
8. What should come next?
1, 2, 4, 10, 16, 40, 64,
Questions 9-12 are based on the following :
Three adults – Roberto, Sarah and Vicky – will be traveling in a van with five children – Freddy, Hillary, Jonathan, Lupe, and Marta. The van has a driver’s seat and one passenger seat in the front, and two benches behind the front seats, one beach behind the other. Each bench has room for exactly three people. Everyone must sit in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench.
Either Roberto or Sarah must sit in the driver’s seat.
Jonathan must sit immediately beside Marta.
9. Of the following, who can sit in the front passenger seat ?
(a) Jonathan (b) Lupe (c) Roberto (d) Sarah (e) Vicky
10. Which of the following groups of three can sit together on a bench?
(a) Freddy, Jonathan and Marta (b) Freddy, Jonathan and Vicky
(c) Freddy, Sarah and Vicky (d) Hillary, Lupe and Sarah
(e) Lupe, Marta and Roberto
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11. If Freddy sits immediately beside Vicky, which of the following cannot be true ?
a. Jonathan sits immediately beside Sarah
b. Lupe sits immediately beside Vicky
c. Hillary sits in the front passenger seat
d. Freddy sits on the same bench as Hillary
e. Hillary sits on the same bench as Roberto
12. If Sarah sits on a bench that is behind where Jonathan is sitting, which of the following must be true ?
a. Hillary sits in a seat or on a bench that is in front of where Marta is sitting
b. Lupe sits in a seat or on a bench that is in front of where Freddy is sitting
c. Freddy sits on the same bench as Hillary
d. Lupe sits on the same bench as Sarah
e. Marta sits on the same bench as Vicky
13. Make six squares of the same size using twelve match-sticks. (Hint : You will need an adhesive to arrange the required figure)
14. A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the are of the larger field is greater than the area of the smaller field by what amount?
(a) 6K (b) 8K (c) 12K (d) 7K
15. Nine equal circles are enclosed in a square whose area is 36sq units. Find the area of each circle.
16. There are 9 cards. Arrange them in a 3*3 matrix. Cards are of 4 colors. They are red, yellow, blue, green. Conditions for arrangement: one red card must be in first row or second row. 2 green cards should be in 3rd column. Yellow cards must be in the 3 corners only. Two blue cards must be in the 2nd row. At least one green card in each row.
17. Is z less than w? z and w are real numbers.
(I) z2 = 25
(II) w = 9
To answer the question,
a) Either I or II is sufficient
b) Both I and II are sufficient but neither of them is alone sufficient
c) I & II are sufficient
d) Both are not sufficient
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18. A speaks truth 70% of the time; B speaks truth 80% of the time. What is the probability that both are contradicting each other?
19. In a family 7 children don't eat spinach, 6 don't eat carrot, 5 don't eat beans, 4 don't eat spinach & carrots, 3 don't eat carrot & beans, 2 don't eat beans & spinach. One doesn't eat all 3. Find the no. of children.
20. Anna, Bena, Catherina and Diana are at their monthly business meeting. Their occupations are author, biologist, chemist and doctor, but not necessarily in that order. Diana just told the neighbour, who is a biologist that Catherina was on her way with doughnuts. Anna is sitting across from the doctor and next to the chemist. The doctor was thinking that Bena was a good name for parent's to choose, but didn't say anything. What is each person's occupation? 18
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19
1. It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
2. A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
3. A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.
4. A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?
5. A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.
6. A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.
7. what is a percent of b divided by b percent of a?
(a) a (b) b (c) 1 (d) 10 (d) 100
8. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
9. A tennis marker is trying to put together a team of four players for a tennis tournament out of seven available. males - a, b and c; females – m, n, o and p. All players are of equal ability and there must be at least two males in the team. For a team of four, all players must be able to play with each other under the following restrictions:
b should not play with m,
c should not play with p, and
a should not play with o.
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Which of the following statements must be false?
1. b and p cannot be selected together
2. c and o cannot be selected together
3. c and n cannot be selected together.
10-12. The following figure depicts three views of a cube. Based on this, answer questions 10-12.
6 5 4
1 22 3 6
2
2
3
10. The number on the face opposite to the face carrying 1 is _______ .
11. The number on the faces adjacent to the face marked 5 are _______ .
12. Which of the following pairs does not correctly give the numbers on the opposite faces.
(1) 6,5 (2) 4,1 (3) 1,3 (4) 4,2
13. Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
14. Five boys were climbing a hill. J was following H. R was just ahead of G. K was between G & H. They were climbing up in a column. Who was the second?
15-18 John is undecided which of the four novels to buy. He is considering a spy
thriller, a Murder mystery, a Gothic romance and a science fiction novel. The books are written by Rothko, Gorky, Burchfield and Hopper, not necessary in that order, and published by Heron, Piegon, Blueja and sparrow, not necessary in that order.
(1) The book by Rothko is published by Sparrow.
(2) The Spy thriller is published by Heron.
(3) The science fiction novel is by Burchfield and is not published by Blueja.
(4)The Gothic romance is by Hopper.
15. Pigeon publishes ____________.
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16. The novel by Gorky ________________.
17. John purchases books by the authors whose names come first and third in alphabetical order. He does not buy the books ______.
18. On the basis of the first paragraph and statement (2), (3) and (4) only, it is possible to deduce that
1. Rothko wrote the murder mystery or the spy thriller
2. Sparrow published the murder mystery or the spy thriller
3. The book by Burchfield is published by Sparrow.
19. If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?
20. If point P is on line segment AB, then which of the following is always true?
(1) AP = PB (2) AP > PB (3) PB > AP (4) AB > AP (5) AB > AP + PB
21. All men are vertebrates. Some mammals are vertebrates. Which of the following conclusions drawn from the above statement is correct.
All men are mammals
All mammals are men
Some vertebrates are mammals.
None
22. Which of the following statements drawn from the given statements are correct?
Given:
All watches sold in that shop are of high standard. Some of the HMT watches are sold in that shop.
a) All watches of high standard were manufactured by HMT.
b) Some of the HMT watches are of high standard.
c) None of the HMT watches is of high standard.
d) Some of the HMT watches of high standard are sold in that shop.
23-27.
1. Ashland is north of East Liverpool and west of Coshocton.
2. Bowling green is north of Ashland and west of Fredericktown.
3. Dover is south and east of Ashland.
4. East Liverpool is north of Fredericktown and east of Dover.
5. Fredericktown is north of Dover and west of Ashland.
6. Coshocton is south of Fredericktown and west of Dover.
23. Which of the towns mentioned is furthest of the north – west
(a) Ashland (b) Bowling green (c) Coshocton
(d) East Liverpool (e) Fredericktown
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24. Which of the following must be both north and east of Fredericktown?
(a) Ashland (b) Coshocton (c) East Liverpool
I a only II b only III c only IV a & b V a & c
25. Which of the following towns must be situated both south and west of at least one other town?
A. Ashland only
B. Ashland and Fredericktown
C. Dover and Fredericktown
D. Dover, Coshocton and Fredericktown
E. Coshocton, Dover and East Liverpool.
26. Which of the following statements, if true, would make the information in the numbered statements more specific?
(a) Coshocton is north of Dover.
(b) East Liverpool is north of Dover
(c) Ashland is east of Bowling green.
(d) Coshocton is east of Fredericktown
(e) Bowling green is north of Fredericktown
27. Which of the numbered statements gives information that can be deduced from one or more of the other statements?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 6
28. Eight friends Harsha, Fakis, Balaji, Eswar, Dhinesh, Chandra, Geetha, and Ahmed are sitting in a circle facing the center. Balaji is sitting between Geetha and Dhinesh. Harsha is third to the left of Balaji and second to the right of Ahmed. Chandra is sitting between Ahmed and Geetha and Balaji and Eshwar are not sitting opposite to each other. Who is third to the left of Dhinesh?
29. If every alternative letter starting from B of the English alphabet is written in small letter, rest all are written in capital letters, how the month “ September” be written.
(1) SeptEMbEr (2) SEpTeMBEr (3) SeptembeR
(4) SepteMber (5) None of the above.
30. The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______.
31. It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?
32. Which of the following is larger than 3/5? 4
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(1) ½ (2) 39/50 (3) 7/25 (4) 3/10 (5) 59/100
33. The number that does not have a reciprocal is ____________.
34. There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.
35. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
Answers:
1. Answer:
30 days.
Explanation:
Before:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work = (75 * 20) / 50 = 30
2. Answer:
0 %
Explanation:
Since 3x / 2 = x / (2 / 3)
3. Answer:
5.3 %
Explanation:
He sells 950 grams of pulses and gains 50 grams.
If he sells 100 grams of pulses then he will gain (50 / 950) *100 = 5.26
4. Answer:
250 lines of codes
5. Answer:
7 days
Explanation:
The equation portraying the given problem is:
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10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.
6. Answer:
150 men.
Explanation:
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)
The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.
So we get the equation
(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working after the 90th day.
We get x = 225
Since we have 75 men already, it is enough to add only 150 men.
7. Answer:
(c) 1
Explanation:
a percent of b : (a/100) * b
b percent of a : (b/100) * a
a percent of b divided by b percent of a : ((a / 100 )*b) / (b/100) * a )) = 1
8. Answer:
Cost price of horse = Rs. 400 & the cost price of cart = 200.
Explanation:-
Let x be the cost price of the horse and y be the cost price of the cart.
In the first sale there is no loss or profit. (i.e.) The loss obtained is equal to the gain.
Therefore (10/100) * x = (20/100) * y
X = 2 * y -----------------(1)
In the second sale, he lost Rs. 10. (i.e.) The loss is greater than the profit by Rs. 10.
Therefore (5 / 100) * x = (5 / 100) * y + 10 -------(2)
Substituting (1) in (2) we get
(10 / 100) * y = (5 / 100) * y + 10
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(5 / 100) * y = 10
y = 200
From (1) 2 * 200 = x = 400
9. Answer:
3.
Explanation:
Since inclusion of any male player will reject a female from the team. Since there should be four member in the team and only three males are available, the girl, n should included in the team always irrespective of others selection.
10. Answer:
5
11. Answer:
1,2,3 & 4
12. Answer:
B
13. Answer:
11 & 9 apples per tree.
Explanation:
Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that a + 1 = b + 3 = c – 1 = d + 3 = e – 6
But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3.
Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively.
Therefore 11 x – 1 = 13 y + 3
By trial and error method, we get the value for x and y as 11 and 9
14. Answer:
G.
Explanation:
The order in which they are climbing is R – G – K – H – J
15 – 18
Answer:
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow
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Explanation:
Given
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow
Since Blueja doesn’t publish the novel by Burchfield and Heron publishes the novel spy thriller, Piegon publishes the novel by Burchfield.
Since Hopper writes Gothic romance and Heron publishes the novel spy thriller, Blueja publishes the novel by Hopper.
Since Heron publishes the novel spy thriller and Heron publishes the novel by Gorky, Gorky writes Spy thriller and Rathko writes Murder mystery.
19. Answer:
451 times.
Explanation:
There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
20. Answer:
(4)
Explanation:
P
A B
Since p is a point on the line segment AB, AB > AP
21. Answer: (c)
22. Answer: (b) & (d).
Ahmed
23 - 27.Answer:
Fakis Chandra
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28. Answer:Fakis
Explanation: Harsha Geetha
Eswar Balaji
Dhinesh
29. Answer:
(5).
Explanation:
Since every alternative letter starting from B of the English alphabet is written in small letter, the letters written in small letter are b, d, f...
In the first two answers the letter E is written in both small & capital letters, so they are not the correct answers. But in third and fourth answers the letter is written in small letter instead capital letter, so they are not the answers.
30. Answer:
x = 4
Explanation:
Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
(i.e.) 4x + 8 = 6x
(i.e.) 2x = 8 τ x = 4.
31. Answer:
(y – 2) / y.
Explanation:
To type a manuscript karthik took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y
32. Answer:
(2)
33. Answer:
1
Explanation:
One is the only number exists without reciprocal because the reciprocal of one is one itself.
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34. Answer:
Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars.
Explanation:
Sudhir Arvind Gauri
Finally 24 24 24
Before Gauri’s transaction 12 12 48
Before Arvind’s transaction 6 42 24
Before Sudhir’ s transaction 39 21 12
35. Answer:
Cost price of horse: Rs. 400 &
Cost price of cart: Rs. 200
Explanation:
Let x be the cost of horse & y be the cost of the cart.
10 % of loss in selling horse = 20 % of gain in selling the cart
Therefore (10 / 100) * x = (20 * 100) * y
τ x = 2y -----------(1)
5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart.
Therefore (5 / 100) * x - 10 = (5 / 100) * y
τ 5x - 1000 = 5y
Substituting (1)
10y - 1000 = 5y
5y = 1000
y = 200
x = 400 from (1)
Exercise 2.1
For the following, find the next term in the series
1. 6, 24, 60,120, 210
a) 336 b) 366 c) 330 d) 660
Answer : a) 336
Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ..... ( '.' means product)
2. 1, 5, 13, 25
Answer : 41
Explanation : The series is of the form 0^2+1^2, 1^2+2^2,...
3. 0, 5, 8, 17
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Answer : 24
Explanation : 1^2-1, 2^2+1, 3^2-1, 4^2+1, 5^2-1
4. 1, 8, 9, 64, 25 (Hint : Every successive terms are related)
Answer : 216
Explanation : 1^2, 2^3, 3^2, 4^3, 5^2, 6^3
5. 8,24,12,36,18,54
Answer : 27
6. 71,76,69,74,67,72
Answer : 67
7. 5,9,16,29,54
Answer : 103
Explanation : 5*2-1=9; 9*2-2=16; 16*2-3=29; 29*2-4=54; 54*2-5=103
8. 1,2,4,10,16,40,64 (Successive terms are related)
Answer : 200
Explanation : The series is powers of 2 (2^0,2^1,..).
All digits are less than 8. Every second number is in octal number system.
128 should follow 64. 128 base 10 = 200 base 8.
Exercise 2.2
Find the odd man out.
1. 3,5,7,12,13,17,19
Answer : 12
Explanation : All but 12 are odd numbers
2. 2,5,10,17,26,37,50,64
Answer : 64
Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65;
3. 105,85,60,30,0,-45,-90
Answer : 0
Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90;
Exercise 3
Solve the following.
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Engineers Zone
1. What is the number of zeros at the end of the product of the numbers from 1 to 100?
Answer : 127
2. A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
Answer : 1 hr 12 min
Explanation : The fast typist's work done in 1 hr = 1/2
The slow typist's work done in 1 hr = 1/3
If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min
3. Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)
Answer : 101
Explanation : Total score after 50 innings = 50*50 = 2500
Total score after 51 innings = 51*51 = 2601
So, runs made in the 51st innings = 2601-2500 = 101
If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.
4. Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?
Answer : 4
5. What can you conclude from the statement : All green are blue, all blue are red. ?
(i) some blue are green
(ii) some red are green
(iii) some green are not red
(iv) all red are blue
(a) i or ii but not both
(b) i & ii only
(c) iii or iv but not both
(d) iii & iv
Answer : (b)
6. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?
Answer : 3.5 inches
Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate
(22/7)*4*4*h = 8*11*2
h = 7/2 = 3.5
12
Engineers Zone
7. What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?
Answer : 35392
Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed.
The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.
112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392
8. If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ...... upto infinity.
Answer : 4
Explanation : Let x = s(12+s(12+s(12+.....
We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.
9. A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?
Answer : 16/3 inches
Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased.
So, the effect on increasing height is equal to the effect on increasing the radius.
i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3
Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches.
10. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?
Answer : 1, 3, 9, 27, 81, 243 (All powers of 3)
11. Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus?
Answer : 84 years
Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
12 . If time at this moment is 9 P.M., what will be the time 23999999992 hours later?
Answer : 1 P.M.
Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M.
13. How big will an angle of one and a half degree look through a glass that magnifies things three times?
Answer : 1 1/2 degrees
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Engineers Zone
Explanation : The magnifying glass cannot increase the magnitude of an angle.
14. Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number.
Answer: 8, 12, 5, 20
Explanation: a + b + c + d =45; a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2); b-4 + b + (b-2)/2 + 2(b-2) = 45;
15. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.
Answer : 37 1/2
Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min
Avg speed = (60*120)/192 = 37 1/2
Questions 16 and 17 are based on the following :
Five executives of European Corporation hold a Conference in Rome
Mr. A converses in Spanish & Italian
Mr. B, a spaniard, knows English also
Mr. C knows English and belongs to Italy
Mr. D converses in French and Spanish
Mr. E , a native of Italy knows French
16. Which of the following can act as interpreter if Mr. C & Mr. D wish to converse
a) only Mr. A b) Only Mr. B c) Mr. A & Mr. B d) Any of the other three
Answer : d) Any of the other three.
Explanation : From the data given, we can infer the following.
A knows Spanish, Italian
B knows Spanish, English
C knows Italian, English
D knows Spanish, French
E knows Italian, French
To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish, English&French
A, B, and E know atleast one of the combinations.
17. If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in
a) English & French b) Italian & Spanish c) English & French d) French & Italian
Answer : b) Italian & Spanish
Explanation : No of executives who know
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Engineers Zone
i) English is 2
ii) Spanish is 3
iii) Italian is 3
iv) French is 2
Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian.
18. What is the sum of the first 25 natural odd numbers?
Answer : 625
Explanation : The sum of the first n natural odd nos is square(n).
1+3 = 4 = square(2) 1+3+5 = 9 = square(3)
19. The sum of any seven consecutive numbers is divisible by
a) 2 b) 7 c) 3 d) 11
Exercise 3
Try the following.
1. There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25?
2. A man sailed off from the North Pole. After covering 2,000 miles in one direction he turned West, sailed 2,000 miles, turned North and sailed ahead another 2,000 miles till he met his friend. How far was he from the North Pole and in what direction?
3. Here is a series of comments on the ages of three persons J, R, S by themselves.
S : The difference between R's age and mine is three years.
J : R is the youngest.
R : Either I am 24 years old or J 25 or S 26.
J : All are above 24 years of age.
S : I am the eldest if and only if R is not the youngest.
R : S is elder to me.
J : I am the eldest.
R : S is not 27 years old.
S : The sum of my age and J's is two more than twice R's age.
One of the three had been telling a lie throughout whereas others had spoken the truth. Determine the ages of S,J,R.
15
Engineers Zone
4. In a group of five people, what is the probability of finding two persons with the same month of birth?
5. A father and his son go out for a 'walk-and-run' every morning around a track formed by an equilateral triangle. The father's walking speed is 2 mph and his running speed is 5 mph. The son's walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other?
6. The Director of Medical Services was on his annual visit to the ENT Hospital. While going through the out patients' records he came across the following data for a particular day : " Ear consultations 45; Nose 50; Throat 70; Ear and Nose 30; Nose and Throat 20; Ear and Throat 30; Ear, Nose and Throat 10; Total patients 100." Then he came to the conclusion that the records were bogus. Was he right?
7. Amongst Ram, Sham and Gobind are a doctor, a lawyer and a police officer. They are married to Radha, Gita and Sita (not in order). Each of the wives have a profession. Gobind's wife is an artist. Ram is not married to Gita. The lawyer's wife is a teacher. Radha is married to the police officer. Sita is an expert cook. Who's who?
8. What should come next?
1, 2, 4, 10, 16, 40, 64,
Questions 9-12 are based on the following :
Three adults – Roberto, Sarah and Vicky – will be traveling in a van with five children – Freddy, Hillary, Jonathan, Lupe, and Marta. The van has a driver’s seat and one passenger seat in the front, and two benches behind the front seats, one beach behind the other. Each bench has room for exactly three people. Everyone must sit in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench.
Either Roberto or Sarah must sit in the driver’s seat.
Jonathan must sit immediately beside Marta.
9. Of the following, who can sit in the front passenger seat ?
(a) Jonathan (b) Lupe (c) Roberto (d) Sarah (e) Vicky
10. Which of the following groups of three can sit together on a bench?
(a) Freddy, Jonathan and Marta (b) Freddy, Jonathan and Vicky
(c) Freddy, Sarah and Vicky (d) Hillary, Lupe and Sarah
(e) Lupe, Marta and Roberto
16
Engineers Zone
11. If Freddy sits immediately beside Vicky, which of the following cannot be true ?
a. Jonathan sits immediately beside Sarah
b. Lupe sits immediately beside Vicky
c. Hillary sits in the front passenger seat
d. Freddy sits on the same bench as Hillary
e. Hillary sits on the same bench as Roberto
12. If Sarah sits on a bench that is behind where Jonathan is sitting, which of the following must be true ?
a. Hillary sits in a seat or on a bench that is in front of where Marta is sitting
b. Lupe sits in a seat or on a bench that is in front of where Freddy is sitting
c. Freddy sits on the same bench as Hillary
d. Lupe sits on the same bench as Sarah
e. Marta sits on the same bench as Vicky
13. Make six squares of the same size using twelve match-sticks. (Hint : You will need an adhesive to arrange the required figure)
14. A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the are of the larger field is greater than the area of the smaller field by what amount?
(a) 6K (b) 8K (c) 12K (d) 7K
15. Nine equal circles are enclosed in a square whose area is 36sq units. Find the area of each circle.
16. There are 9 cards. Arrange them in a 3*3 matrix. Cards are of 4 colors. They are red, yellow, blue, green. Conditions for arrangement: one red card must be in first row or second row. 2 green cards should be in 3rd column. Yellow cards must be in the 3 corners only. Two blue cards must be in the 2nd row. At least one green card in each row.
17. Is z less than w? z and w are real numbers.
(I) z2 = 25
(II) w = 9
To answer the question,
a) Either I or II is sufficient
b) Both I and II are sufficient but neither of them is alone sufficient
c) I & II are sufficient
d) Both are not sufficient
17
Engineers Zone
18. A speaks truth 70% of the time; B speaks truth 80% of the time. What is the probability that both are contradicting each other?
19. In a family 7 children don't eat spinach, 6 don't eat carrot, 5 don't eat beans, 4 don't eat spinach & carrots, 3 don't eat carrot & beans, 2 don't eat beans & spinach. One doesn't eat all 3. Find the no. of children.
20. Anna, Bena, Catherina and Diana are at their monthly business meeting. Their occupations are author, biologist, chemist and doctor, but not necessarily in that order. Diana just told the neighbour, who is a biologist that Catherina was on her way with doughnuts. Anna is sitting across from the doctor and next to the chemist. The doctor was thinking that Bena was a good name for parent's to choose, but didn't say anything. What is each person's occupation? 18
Engineers Zone
19
Sample On-line Test Questions 1
Select the most appropriate answer from the given choices:
Aptitude Test Questions:
1. Three types of tea (namely a, b and c) costs Rs. 95/kg, Rs. 100/kg and Rs. 70/kg respectively. How many Kg. of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of band c are equal ?
A. 70,15,15 B. 50,25,25 C. 60,20,20 D. 40,30,30 Ans. B
2. A father is 30 years older than his son, however he will be only thrice as old as the son after 5 years, what is the father's present age ? A. 40 yrs B. 30 yrs C. 50 yrs D. None of the above Ans. A
3. (1/10)18 - (1/10)20 = ?
A. 99/1020 B. 99/10 C. 0.9 D. None of the above Ans. A
4. There are 200 questions on a 3 hr examination. Among these questions
are 50 mathematics problems. It is suggested that twice as much time be
spent on each math’s problem as for each other question.
How many minutes should be spent on mathematics problems? A. 36 B. 72 C. 60 D. 100 Ans. B
5. taxonomy : classification :: ? A. etymology : derivation B. autonomy : authorization C. economy : rationalization D. tautology : justification E. ecology : urbanization Ans. A
6. Six swimmers A, B, C, D, E, F compete in a race. The outcome is as follows.
i. B does not win. ii. Only two swimmers separate E & D iii. A is behind D & E iv. B is ahead of E, with one swimmer intervening v. F is a head of D. Who stood fifth in the race?
A. A B. B C. C D. D E. E Ans. E
Technology Stream Specific Questions:
7. Which layer in the OSI model deals with the error correction ?
A. Application Layer
B. Network Layer
C. Data Link Layer
D. None of the above Ans. C
8. Which language is used to define the integrity constraints ?
A. DDL
B. DML
C. DCL
D. DLM Ans. A
9. Execution of RST 0 instruction by 8085 ____________.
A. Clears all CPU registers
B. Resets the stack pointer
C. Sends out an Interrupt acknowledgement signal
D. Clears the program counter Ans. D
10. Made from a variety of materials, such as carbon, which of the following inhibits the flow of current ?
A. Choke
B. Inductor
C. Resistor
D. Capacitor Ans. C
Aptitude Test Questions:
1. Three types of tea (namely a, b and c) costs Rs. 95/kg, Rs. 100/kg and Rs. 70/kg respectively. How many Kg. of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of band c are equal ?
A. 70,15,15 B. 50,25,25 C. 60,20,20 D. 40,30,30 Ans. B
2. A father is 30 years older than his son, however he will be only thrice as old as the son after 5 years, what is the father's present age ? A. 40 yrs B. 30 yrs C. 50 yrs D. None of the above Ans. A
3. (1/10)18 - (1/10)20 = ?
A. 99/1020 B. 99/10 C. 0.9 D. None of the above Ans. A
4. There are 200 questions on a 3 hr examination. Among these questions
are 50 mathematics problems. It is suggested that twice as much time be
spent on each math’s problem as for each other question.
How many minutes should be spent on mathematics problems? A. 36 B. 72 C. 60 D. 100 Ans. B
5. taxonomy : classification :: ? A. etymology : derivation B. autonomy : authorization C. economy : rationalization D. tautology : justification E. ecology : urbanization Ans. A
6. Six swimmers A, B, C, D, E, F compete in a race. The outcome is as follows.
i. B does not win. ii. Only two swimmers separate E & D iii. A is behind D & E iv. B is ahead of E, with one swimmer intervening v. F is a head of D. Who stood fifth in the race?
A. A B. B C. C D. D E. E Ans. E
Technology Stream Specific Questions:
7. Which layer in the OSI model deals with the error correction ?
A. Application Layer
B. Network Layer
C. Data Link Layer
D. None of the above Ans. C
8. Which language is used to define the integrity constraints ?
A. DDL
B. DML
C. DCL
D. DLM Ans. A
9. Execution of RST 0 instruction by 8085 ____________.
A. Clears all CPU registers
B. Resets the stack pointer
C. Sends out an Interrupt acknowledgement signal
D. Clears the program counter Ans. D
10. Made from a variety of materials, such as carbon, which of the following inhibits the flow of current ?
A. Choke
B. Inductor
C. Resistor
D. Capacitor Ans. C
TCE PAPER ON 10TH JULY AT NIT,CALICUT
Paper Type : Whole Testpaper Test Date : 10 July 2008
TCE PAPER ON 10TH JULY AT NIT,CALICUT
hi friends this is J.Vishnu mohan reddy M.Tech second year from NIT Calicut.Morning 10am started with PPT followed by written test.we had TCE Engg Written test on 10/07/2008. first let me say selection procedure
Written test of Duration 1hr 30 Aptitude questions and 30 technical questions.Each half an hour given one after other.
Aptitude questions: 3 sections. Verbal section 10 questions Numerical section 10 questions. Reasoning section 10 questions.
Verbal 3 questions 4 sentences given we need to place them n order 4 meaning 1) abundancy i remember only this 2 questions with fill in the blanks.
Numerical section All questions are easy.form percentage profit and loss Partnership and one averages problem they are easy. we can write if we prepare R.S Agar Val
Reasoning section 10 questions. Puzzle test given with 4following 4 questions.
There are 6 rooms each side 3 rooms facing 3 rooms opposite side. C and e rooms are right side of corridor. D room is opposite to C room. E should not be any corner. E and F are in same side like these conditions are given.Followed by 4 questions.
2 questions are given on below one. 2 machines can produce P& Q products independently.
Each machine can work for 8 hours each day. The time taken by each machine is given by as follows.
Machine
M1
M2
P
10minutes
8 minutes
Q
6 minutes
6 minutes
QUESTIONS 1) How many products can be produced in day by two machines. a) 240 b) 360 c)120 d)720 2) Minimum time taken by the machine to produce 48n products. a) 7 hr 10min b) 6 hr 15 min c) 4 hr 10 min I got 3 hr 10 minutes as answer. And questions are given from reasoning are easy.We wrote in technical paper in Instrumentation& Specialization.Total 30 questions. 6 questions are from PID controllers. And remaining questions are on instruments Questions are like this 1) if proportional band is 200% then gain of the system is a) 200 b) 100 c)2 d)0.5 2) Integral controller is used for a) to increase offset b) to increase dead band c) to decrease oscillations. 3) Proportional controller used for 4) What is dead band 5) Bio directional meter a) Magnetic flow meter b) Thermo meter c) Turbulence meter. Etc 6) if specific gravity is 3.546kg/cm2 then density is equal to a) 3.546kg/m3 b) 3.546kg/mm3 c) 3.456gm/mm3 like this d) 7) Viscosity is measured in
Like this they are easy those who knows little bit about instrumentation.We are waiting for results. Today 4pm they will give. Paper Type : General - other Test Date : 19 July 2007
TCE PAPER ON 9TH JULY,2007
Hi friend TCE is totally depends on your core knowledge.its very nice and tata group of company.I am
going to share my feeling nd some question related to its recruitment. There are three round.....
1-Written......in which three section r there
1>English....(easy one)
2>Analytical reasoning (time taken)
3>Aptitude (time taken) All this paper having 10 quation each nd time is 30 min. Next section is your branch related section.....if electrical then electrical...nd so on In this section also 30 quation 30 min. quation was triky...so plz b fast nd accurate. after this written test a tecnical test is there.nd then some student r called for hr round nd thos called they got selected. so all the best to all of u. sample quation.... English> 2quation from antonyms nd 2 from synonyms. jumbled sentense arrengement....2 q. fill in the blanks.... Analytical reasoning Graph is given related to that sm quation.... mathamatical resoning..(follow rs agrawal reasoning) nd in aptitude it is series based nd profit nd loss rs agrawal aptitude book is suficient for this sm cut off point r there out of 300 in our pooled campus only 40 student r selected after written test. Technical..... Genrally they ask ur 4 fav subject.(i m telling about electrical) they ask quation from ur each fav sub throughly...so plz prepared well ur fav subject. as i told electrical machine,TD, basic electronics nd basic electrical o he sak draw the equivalent cirkt diagram of 3 phase induction motor,draw its torque speed charectersticknd bla bla....what is full form of IGBT,what is the diff. bit IGBT nd scr......nd lot of quation....... b confident. dont bluff.....u will through...after that i was called for hr....my hr round goes 50 min in open air....they r very friendly....make us very easy....nd finally result was declared nd out of 2 electrical i m one of them .finaly they selected 6 student 2 from ee, 2 from mech, 2 from civil. so all the best guyyyy I think this must help you to guidline for TCE prepration . Paper Type : General - other Test Date : 23 August 2007
TCE PAPER ON 23rd AUGUST AT HYDERABAD
Hi frends.........,
This is K.Rupa from BHOJ REDDY ENGG COLL for WOMEN, Hyderabad. We attended Tata Chemical as an off-campous which held in TKR coll, Hyd. There r mainly four stages in the selection procedure.
They are like (1) Written Test( The test consist of 2 parts Aptitude and Technical which is purely concept based ) Duration is 1hr( 30 min Aptitude & 30 min Technical ). Aptitude contain-30 questions & Technical contain-50 questions. (2) G.D (3) Technical Interview. (4) H.R
Aptitude section: This basically contain 5 verbal ques'n( synonyms-3 & antonims-2 ). This are so easy to be answered i got (1) FEIGN, (2)SPECIFIC, (3)TEMPLET sorry i dont remember this..., (4) TEDUOUS, (5)this is also so simple... After this there are 5 ques'n based on Data Interpretation. They r so easy no need to worry about that later i got some 10 ques'ns based on algebra, like... (1) cos 45= ? (2) If a man covers 750km in 2hrs, then much dis can he cover in 5hrs 45 min (3) Two trains problem, moving in opposite directions with some velocities 500 & 700 km/hr. The dis is 2400. then find the time taken for them to meet. (4) There are many ques'n based on trains ...aprox 3-4 ques'n there are some ques'n based on areas like area of the sphere, cube is so and so ..... then find edge later i got some 10 ques'ns based on...
i dont know exactly but the que'ns are like (1) The distance b/w the two circle present on the scale ( on the scale there r some circles of same size, separated by same distance ) (2) The scale contain some readings and some instrument is beside that, then what fraction of scale is covered by instrument. (3) Some weight of 80kg is placed at one end of the pully, then how much wt must be added on the other side of the pully to make it balance.... the balanace is not placed exactly at the center , this is dis dependent the rest of the questions are also easy.......to say aptitude section is so easy
Technical section: This is so hard one. in this there will be 50q to be answ in just 30 min. this section basically include main concepts, there is no need to worry for the people who r studing for GATE. (1) Pecklet no. def (2)They had some question from the stuff we study in +2 like ideal gas equation, vander wals eqn etc. (3) nusselt no. is used when ........ (4) If temp inc then what happens to viscosity? (5) Cox chart is used in ....Distillation, evaporation, drying r none (6) Renolds no. is? (7) Inertial forces to drag forces is called which no.? (8) The stage belo saturation is called?
(9) Throtling is the process dependent on (options)Temp r Press r Volume (10) which cycle is efficient (option) otto , air....
The rest are also easy.... I am not giving u the solutions for this question's bcz, i haven't got selected to TCE. I wrote the written so perfectly but the selection process is some what different yar so luck also matters alot. for us i thought it is the random selection. we waited till 8 in the evening but unable to find a good news. but this sould nt repeat for u people that is the basic reason y i am writing this questions. prepare well it is better to take any GATE book and check out the basic concepts before attemption the exam.
TCE PAPER ON 10TH JULY AT NIT,CALICUT
hi friends this is J.Vishnu mohan reddy M.Tech second year from NIT Calicut.Morning 10am started with PPT followed by written test.we had TCE Engg Written test on 10/07/2008. first let me say selection procedure
Written test of Duration 1hr 30 Aptitude questions and 30 technical questions.Each half an hour given one after other.
Aptitude questions: 3 sections. Verbal section 10 questions Numerical section 10 questions. Reasoning section 10 questions.
Verbal 3 questions 4 sentences given we need to place them n order 4 meaning 1) abundancy i remember only this 2 questions with fill in the blanks.
Numerical section All questions are easy.form percentage profit and loss Partnership and one averages problem they are easy. we can write if we prepare R.S Agar Val
Reasoning section 10 questions. Puzzle test given with 4following 4 questions.
There are 6 rooms each side 3 rooms facing 3 rooms opposite side. C and e rooms are right side of corridor. D room is opposite to C room. E should not be any corner. E and F are in same side like these conditions are given.Followed by 4 questions.
2 questions are given on below one. 2 machines can produce P& Q products independently.
Each machine can work for 8 hours each day. The time taken by each machine is given by as follows.
Machine
M1
M2
P
10minutes
8 minutes
Q
6 minutes
6 minutes
QUESTIONS 1) How many products can be produced in day by two machines. a) 240 b) 360 c)120 d)720 2) Minimum time taken by the machine to produce 48n products. a) 7 hr 10min b) 6 hr 15 min c) 4 hr 10 min I got 3 hr 10 minutes as answer. And questions are given from reasoning are easy.We wrote in technical paper in Instrumentation& Specialization.Total 30 questions. 6 questions are from PID controllers. And remaining questions are on instruments Questions are like this 1) if proportional band is 200% then gain of the system is a) 200 b) 100 c)2 d)0.5 2) Integral controller is used for a) to increase offset b) to increase dead band c) to decrease oscillations. 3) Proportional controller used for 4) What is dead band 5) Bio directional meter a) Magnetic flow meter b) Thermo meter c) Turbulence meter. Etc 6) if specific gravity is 3.546kg/cm2 then density is equal to a) 3.546kg/m3 b) 3.546kg/mm3 c) 3.456gm/mm3 like this d) 7) Viscosity is measured in
Like this they are easy those who knows little bit about instrumentation.We are waiting for results. Today 4pm they will give. Paper Type : General - other Test Date : 19 July 2007
TCE PAPER ON 9TH JULY,2007
Hi friend TCE is totally depends on your core knowledge.its very nice and tata group of company.I am
going to share my feeling nd some question related to its recruitment. There are three round.....
1-Written......in which three section r there
1>English....(easy one)
2>Analytical reasoning (time taken)
3>Aptitude (time taken) All this paper having 10 quation each nd time is 30 min. Next section is your branch related section.....if electrical then electrical...nd so on In this section also 30 quation 30 min. quation was triky...so plz b fast nd accurate. after this written test a tecnical test is there.nd then some student r called for hr round nd thos called they got selected. so all the best to all of u. sample quation.... English> 2quation from antonyms nd 2 from synonyms. jumbled sentense arrengement....2 q. fill in the blanks.... Analytical reasoning Graph is given related to that sm quation.... mathamatical resoning..(follow rs agrawal reasoning) nd in aptitude it is series based nd profit nd loss rs agrawal aptitude book is suficient for this sm cut off point r there out of 300 in our pooled campus only 40 student r selected after written test. Technical..... Genrally they ask ur 4 fav subject.(i m telling about electrical) they ask quation from ur each fav sub throughly...so plz prepared well ur fav subject. as i told electrical machine,TD, basic electronics nd basic electrical o he sak draw the equivalent cirkt diagram of 3 phase induction motor,draw its torque speed charectersticknd bla bla....what is full form of IGBT,what is the diff. bit IGBT nd scr......nd lot of quation....... b confident. dont bluff.....u will through...after that i was called for hr....my hr round goes 50 min in open air....they r very friendly....make us very easy....nd finally result was declared nd out of 2 electrical i m one of them .finaly they selected 6 student 2 from ee, 2 from mech, 2 from civil. so all the best guyyyy I think this must help you to guidline for TCE prepration . Paper Type : General - other Test Date : 23 August 2007
TCE PAPER ON 23rd AUGUST AT HYDERABAD
Hi frends.........,
This is K.Rupa from BHOJ REDDY ENGG COLL for WOMEN, Hyderabad. We attended Tata Chemical as an off-campous which held in TKR coll, Hyd. There r mainly four stages in the selection procedure.
They are like (1) Written Test( The test consist of 2 parts Aptitude and Technical which is purely concept based ) Duration is 1hr( 30 min Aptitude & 30 min Technical ). Aptitude contain-30 questions & Technical contain-50 questions. (2) G.D (3) Technical Interview. (4) H.R
Aptitude section: This basically contain 5 verbal ques'n( synonyms-3 & antonims-2 ). This are so easy to be answered i got (1) FEIGN, (2)SPECIFIC, (3)TEMPLET sorry i dont remember this..., (4) TEDUOUS, (5)this is also so simple... After this there are 5 ques'n based on Data Interpretation. They r so easy no need to worry about that later i got some 10 ques'ns based on algebra, like... (1) cos 45= ? (2) If a man covers 750km in 2hrs, then much dis can he cover in 5hrs 45 min (3) Two trains problem, moving in opposite directions with some velocities 500 & 700 km/hr. The dis is 2400. then find the time taken for them to meet. (4) There are many ques'n based on trains ...aprox 3-4 ques'n there are some ques'n based on areas like area of the sphere, cube is so and so ..... then find edge later i got some 10 ques'ns based on...
i dont know exactly but the que'ns are like (1) The distance b/w the two circle present on the scale ( on the scale there r some circles of same size, separated by same distance ) (2) The scale contain some readings and some instrument is beside that, then what fraction of scale is covered by instrument. (3) Some weight of 80kg is placed at one end of the pully, then how much wt must be added on the other side of the pully to make it balance.... the balanace is not placed exactly at the center , this is dis dependent the rest of the questions are also easy.......to say aptitude section is so easy
Technical section: This is so hard one. in this there will be 50q to be answ in just 30 min. this section basically include main concepts, there is no need to worry for the people who r studing for GATE. (1) Pecklet no. def (2)They had some question from the stuff we study in +2 like ideal gas equation, vander wals eqn etc. (3) nusselt no. is used when ........ (4) If temp inc then what happens to viscosity? (5) Cox chart is used in ....Distillation, evaporation, drying r none (6) Renolds no. is? (7) Inertial forces to drag forces is called which no.? (8) The stage belo saturation is called?
(9) Throtling is the process dependent on (options)Temp r Press r Volume (10) which cycle is efficient (option) otto , air....
The rest are also easy.... I am not giving u the solutions for this question's bcz, i haven't got selected to TCE. I wrote the written so perfectly but the selection process is some what different yar so luck also matters alot. for us i thought it is the random selection. we waited till 8 in the evening but unable to find a good news. but this sould nt repeat for u people that is the basic reason y i am writing this questions. prepare well it is better to take any GATE book and check out the basic concepts before attemption the exam.
The MAT conducted on 3rd May 2009 was the last hope for the MBA aspirants to get a admission in a session starting from July 2009.
The MAT conducted on 3rd May 2009 was the last hope for the MBA aspirants to get a admission in a session starting from July 2009.
This time 444 management institutes are taking the results of MAT.
The pattern of MAT was as usual total 200 jumbled questions with 40 questions from each test area; Reading Comprehension and
English Usage (RC and EU), Quantitative Aptitude (QA), Logical Reasoning (LR), Data Interpretation and Data Sufficiency
(DI and DS) and General Knowledge (GK). The time allowed to solve the paper was 150 minutes. Four alternatives were provided for
each question.
It was declared in the instruction provided in the paper at the last page that each correct answer will carry one mark, while there was
a negative marking of 0.25 marks for each incorrect answer. Total thirteen different sets of test booklets were available there. Overall
level of difficulty of the paper was moderate to easy.
Management Aptitude Test
May 03, 2009
Bird’s Eye View
Total Number of Questions – 200
Total Time – 150 minutes
The Marking Scheme – One mark for each correct anwer. – 0.25 mars for each incorrect answer.
Total Marks – 200
Number of Options – 4
Number of sets Available – 13 (AM)
Sections/Sectional Time Limit – There were no sections and the paper was jumbled.
Medium of marking – Pencil
Breakup–
Topic No. of
Ques.
No. of
Marks
Difficulty
Level
Quantitative Aptitude 39 39 Moderate
Logical Reasoning 41 41 Moderate
Data Interpretation and
Data Sufficiency
40 40 Easy
Reading Comprehension 40 40 Moderate
General Knowledge 40 40
Mix of Easy and
Moderate
Expected CutOffs
– An score of 100+ (out of 160 i.e. excluding GK) should be good to getting AMITY, Christ, Alliance and some
other top BSchools.
(2) of (2) IC : PTpnrMATmay2009
The ideal strategy to solve the paper should be –
1 . In first 1015
minutes scan all the GK questions and attempt the questions on which you are dam sure.
2 . After that start picking good solvable questions from start of the paper.
The questions from CodingDecoding,
Numbers, Fractions, Arithmetic, Para Jumbles, FIBs, Analogies, Data Arrangement,
Syllogism, Data Comparison and the DI sets containing the Pie Charts etc. can be included in this round.
3 . After the first round of attempts, attempt the tougher questions like questions on DI sets containing tables and Bar graph,
questions from Mensuration, Height and Distance, some questions of mixtures, work and time, the strong and weak argument
questions, questions on cubes, reading of RC passages, sentence correction question etc. can be done in this round.
Ideally a student, who is good to select the questions to solve, could attempt 50 to 55 questions in the first hour
itself.
The questions from the areas like Numbers, Fractions, SI and CI, Time Speed and Distance (including Trains), Races,
Averages, Percentages, Work and Time (including Pipes and Cisterns), Profit and Loss, Mixtures, Profit and Loss, Calendar,
Ratio and Proportion, Mensuration, Height and Distances, Probability, Permutation and Combination, were the
representative of QA area. The questions were of moderate level of difficulty. For a well prepared student on an average not more than
11.5
minutes would be required to solve one question of this area.
To check the students' logical and analytical abilities there were questions on Direction Sense, Calendar, Relations, Linear and
Matrix arrangements, StatementAssumption,
StatementConclusion,
CodingDecoding
and Cubes. One could attempt
23+ questions in a time span of 35 minutes from this area.
There were total five RC passages. Total 25 questions were asked on these passages. The themes of the RC passages were on G20,
democratising of electoral system etc. The length of the passages was of approx. 1000 words and 5 questions were asked on
each passage. The questions asked were moderate level of difficulty.
Source of RC Passages –
G20:
Just Glamour and Glitter http://
www.thehindubusinessline.com/2009/04/06/stories/2009040650230900.htm
democratising the electoral system – http://www.hindu.com/2009/04/09/stories/2009040955750800.htm
From EU area there were questions on FIBs, Critical Reasoning, Sentence Correction, Para Jumble and Sentence Correction.
The questions were of moderate level of difficulty.
The GK questions were a mixture of easy and moderate level of difficulty. The questions were on dynamic as well as traditional GK. There
were questions on Economics, Current Affairs, Awards and Prizes, Days. Since this area was only to pass and marks of this will
not be include in merit, an attempt of 1215
questions will be sufficient to achieve the cutoff
for this area.
Best wishes!
This time 444 management institutes are taking the results of MAT.
The pattern of MAT was as usual total 200 jumbled questions with 40 questions from each test area; Reading Comprehension and
English Usage (RC and EU), Quantitative Aptitude (QA), Logical Reasoning (LR), Data Interpretation and Data Sufficiency
(DI and DS) and General Knowledge (GK). The time allowed to solve the paper was 150 minutes. Four alternatives were provided for
each question.
It was declared in the instruction provided in the paper at the last page that each correct answer will carry one mark, while there was
a negative marking of 0.25 marks for each incorrect answer. Total thirteen different sets of test booklets were available there. Overall
level of difficulty of the paper was moderate to easy.
Management Aptitude Test
May 03, 2009
Bird’s Eye View
Total Number of Questions – 200
Total Time – 150 minutes
The Marking Scheme – One mark for each correct anwer. – 0.25 mars for each incorrect answer.
Total Marks – 200
Number of Options – 4
Number of sets Available – 13 (AM)
Sections/Sectional Time Limit – There were no sections and the paper was jumbled.
Medium of marking – Pencil
Breakup–
Topic No. of
Ques.
No. of
Marks
Difficulty
Level
Quantitative Aptitude 39 39 Moderate
Logical Reasoning 41 41 Moderate
Data Interpretation and
Data Sufficiency
40 40 Easy
Reading Comprehension 40 40 Moderate
General Knowledge 40 40
Mix of Easy and
Moderate
Expected CutOffs
– An score of 100+ (out of 160 i.e. excluding GK) should be good to getting AMITY, Christ, Alliance and some
other top BSchools.
(2) of (2) IC : PTpnrMATmay2009
The ideal strategy to solve the paper should be –
1 . In first 1015
minutes scan all the GK questions and attempt the questions on which you are dam sure.
2 . After that start picking good solvable questions from start of the paper.
The questions from CodingDecoding,
Numbers, Fractions, Arithmetic, Para Jumbles, FIBs, Analogies, Data Arrangement,
Syllogism, Data Comparison and the DI sets containing the Pie Charts etc. can be included in this round.
3 . After the first round of attempts, attempt the tougher questions like questions on DI sets containing tables and Bar graph,
questions from Mensuration, Height and Distance, some questions of mixtures, work and time, the strong and weak argument
questions, questions on cubes, reading of RC passages, sentence correction question etc. can be done in this round.
Ideally a student, who is good to select the questions to solve, could attempt 50 to 55 questions in the first hour
itself.
The questions from the areas like Numbers, Fractions, SI and CI, Time Speed and Distance (including Trains), Races,
Averages, Percentages, Work and Time (including Pipes and Cisterns), Profit and Loss, Mixtures, Profit and Loss, Calendar,
Ratio and Proportion, Mensuration, Height and Distances, Probability, Permutation and Combination, were the
representative of QA area. The questions were of moderate level of difficulty. For a well prepared student on an average not more than
11.5
minutes would be required to solve one question of this area.
To check the students' logical and analytical abilities there were questions on Direction Sense, Calendar, Relations, Linear and
Matrix arrangements, StatementAssumption,
StatementConclusion,
CodingDecoding
and Cubes. One could attempt
23+ questions in a time span of 35 minutes from this area.
There were total five RC passages. Total 25 questions were asked on these passages. The themes of the RC passages were on G20,
democratising of electoral system etc. The length of the passages was of approx. 1000 words and 5 questions were asked on
each passage. The questions asked were moderate level of difficulty.
Source of RC Passages –
G20:
Just Glamour and Glitter http://
www.thehindubusinessline.com/2009/04/06/stories/2009040650230900.htm
democratising the electoral system – http://www.hindu.com/2009/04/09/stories/2009040955750800.htm
From EU area there were questions on FIBs, Critical Reasoning, Sentence Correction, Para Jumble and Sentence Correction.
The questions were of moderate level of difficulty.
The GK questions were a mixture of easy and moderate level of difficulty. The questions were on dynamic as well as traditional GK. There
were questions on Economics, Current Affairs, Awards and Prizes, Days. Since this area was only to pass and marks of this will
not be include in merit, an attempt of 1215
questions will be sufficient to achieve the cutoff
for this area.
Best wishes!
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